Interesting question. 'Dran' is originally the short form of 'daran' although you wouldn't replace 'dran' with 'daran'. 'Dran' means here 'at it'. The sentence 'Wir sind spät' would be meaningless in German because you can only be late for something. 'Dran' takes different meanings as place holder.

I had trouble with this one when it was presented in lesson 1.7 (one of the non-guided lessons, so we don't have any interactive audio to help with this word). I added it to My Vocab for further research. From what I see, these are just idiomatic expressions to be memorized. Trying to find meaning behind this one is futile. But feel free to report back if you find anything interesting. Below I give you some references that make me come to that conclusion.

The dictionary here is called Phrase Finder (http://members.rocketlanguages.com/Toolbox/)

You will find "dran" listed there in five phrases.
You will find "spät" listed many more times.

Technically dran is an adverb and spät is an adjective, that helps with the usage, but not meaning...Read MoreHi Britannus,

I had trouble with this one when it was presented in lesson 1.7 (one of the non-guided lessons, so we don't have any interactive audio to help with this word). I added it to My Vocab for further research. From what I see, these are just idiomatic expressions to be memorized. Trying to find meaning behind this one is futile. But feel free to report back if you find anything interesting. Below I give you some references that make me come to that conclusion.

The dictionary here is called Phrase Finder (http://members.rocketlanguages.com/Toolbox/)

You will find "dran" listed there in five phrases.
You will find "spät" listed many more times.

Technically dran is an adverb and spät is an adjective, that helps with the usage, but not meaning.

Wordreference says the same as Paul: http://forum.wordreference.com/showthread.php?t=2667478
[You can roughly translate this dran as at it. You can only be late for something, late for work, late in the shopping mall so all the shops have closed, etc. You cannot be late per se. This dran is a kind of place holder referring to an unspecified goal for which he is late. E.g. Er musste sich mit dem Frühstück beeilen, weil er spät dran war. This mean he had to hurry taking his breakfast because he needs to do something or be somewhere which it not specified.]

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